Classify each description as a parameter or a statistic.
Parameter
Statistic
Answer Bank
A. the mean height of adult males throughout the world
B. of the 75 business owners in five industries surveyed, the proportion who attend business conferences each year
C. the proportion of registered voters in the United States who watch the Presidential debate on television
D. out of 50 rental properties chosen at random in Ohio, the proportion who have maintenance staff living onsite
E. the percentage of automobiles with four doors that are a shade of red
The Correct Answer and Explanation is:
Sure! Here are the classifications for each description, followed by a detailed explanation:
Answer:
A. Parameter
B. Statistic
C. Parameter
D. Statistic
E. Parameter
Explanation:
In statistics, the key distinction between a parameter and a statistic lies in whether the value describes an entire population or a sample drawn from that population.
- Parameter: A numerical value that describes a characteristic of a population — meaning the entire group under consideration.
- Statistic: A numerical value that describes a characteristic of a sample — a subset drawn from the population.
Now let’s look at each example:
A. The mean height of adult males throughout the world
This is describing the mean height of all adult males in the world, which is an entire population. Since it refers to a whole population, this value is a parameter.
B. Of the 75 business owners in five industries surveyed, the proportion who attend business conferences each year
This is data from a sample of 75 business owners surveyed, not the entire population of business owners. Therefore, this is a statistic because it describes a sample.
C. The proportion of registered voters in the United States who watch the Presidential debate on television
This describes the entire population of registered voters in the U.S. It references the whole group rather than a sample, so this is a parameter.
D. Out of 50 rental properties chosen at random in Ohio, the proportion who have maintenance staff living onsite
This is a sample of 50 rental properties chosen randomly, which is a subset of all rental properties in Ohio. Because it comes from a sample, this is a statistic.
E. The percentage of automobiles with four doors that are a shade of red
Assuming this refers to all automobiles with four doors (the entire population), this is a parameter. If it had specified a subset or sample, it would be a statistic, but since no sample is mentioned, it implies the whole group.
Summary
Parameters describe whole populations (e.g., mean height of all adult males worldwide, proportion of all registered voters watching a debate), while statistics describe samples (e.g., survey results from 75 business owners or 50 rental properties). This distinction is fundamental in statistics because it impacts how conclusions are drawn. Parameters are fixed but usually unknown, while statistics are calculated from samples and used to estimate parameters.
Understanding whether a value is a parameter or statistic helps guide appropriate analysis techniques and inference in research and data interpretation.